Finite Group Databasebeta

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C₂³×#3490 #72255582

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

630229 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 8 generators on 22 points:

(3,4);(8,11)(12,14)(16,19)(17,21);(15,16)(17,20)(18,19)(21,22);(9,13)(12,14)(17,21)(20,22);(7,8)(9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22);(5,6);(1,2)(3,4)(5,6);(7,9)(8,12)(10,13)(11,14)(15,17,18,21)(16,20,19,22)

Conjugacy classes & character table

352 conjugacy classes. The character table is too large to display.

Relationships

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((3,4), (8,11)(12,14)(16,19)(17,21), (15,16)(17,20)(18,19)(21,22), (9,13)(12,14)(17,21)(20,22), (7,8)(9,12)(10,11)(13,14)(15,16)(17,20)(18,19)(21,22), (5,6), (1,2)(3,4)(5,6), (7,9)(8,12)(10,13)(11,14)(15,17,18,21)(16,20,19,22));